Monte Carlo Simulations
Monte Carlo experiments are powerful techniques very often used in applied econometric analyses
to asses the small sample behavior of estimator and test statistics. A Monte Carlo experiment
consists in di¤erent parts.
1. De…ne the issue to analyze
2. The data generating process (DGP) where your develop your known process
3. Generating numbers at random
4. Estimation and test statistics for one replication of the loop. Use of procedures
5. Storage and computation of summary statistics over the M replications
To illustrate these di¤erent steps, let us consider the relationship between two independent random
walks (with drifts). Engle and Granger (1987) and Phillips (1996) show that if we regress these
variables on each other, there is a tendency to obtain spurious regressions. This phenomenon is
characterized by values of t􀀀 ratios for which we would reject the null hypothesis of no
relationships at any sensible signi…cance levels. Moreover the R2 are high because of the common
stochastic trends.
For the data generating process (DGP), let us generate the following independent bivariate process: